Flexural capacity of steel reinforced ultra-high performance concrete beams with rectangular section
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摘要: 为研究矩形截面型钢超高性能混凝土(SRUHPC)梁的抗弯特性，制作了4根配筋率为0.8%~1.1%，含钢率为8.7%~15.6%，内置型钢分别为一字型、倒T型与H型的矩形截面SRUHPC梁试件，开展了抗弯极限承载力试验，分析了矩形截面SRUHPC梁试件的损伤机理和破坏模式；基于试验结果与理论推导，提出了矩形截面SRUHPC梁抗弯承载力计算方法，计算了21根矩形截面SRUHPC梁试件和111个有限元计算模型的抗弯承载力，并将计算结果与试验值和有限元计算值进行了对比。分析结果表明：矩形截面SRUHPC梁试件的破坏模式均为适筋受弯破坏，即型钢与受拉纵筋先后屈服，随后受压区UHPC被压碎，且型钢与UHPC可较好地共同工作至试件破坏；内置倒T型钢试件和H型钢试件的承载力和刚度高于内置一字型钢试件，且抗裂性能更好；与其他试件相比，内置H型钢试件中纵筋、UHPC与型钢在相同荷载作用下的应变及其发展速度均较小，因此，在矩形截面SRUHPC梁内的型钢中设置上、下翼缘有助于提高组合梁的抗弯性能；采用提出方法得到的计算结果与试验值和有限元计算值的比值均值分别为0.972和1.035，方差分别为0.009和0.002，研究结果可为矩形截面SRUHPC梁在实际工程中的推广应用和规范、规程的制定提供理论支撑。Abstract: To study the bending resistance characteristics of steel reinforced ultra-high performance concrete (SRUHPC) beams with rectangular section, four SRUHPC beam specimens with rectangular section were fabricated, with the reinforcing ratios ranging from 0.8% to 1.1% and the steel ratios ranging from 8.7% to 15.6%. The embedded steels are I-shaped, inverted T-shaped, and H-shaped. Flexural ultimate capacity tests were conducted to analyze the damage mechanism and failure modes of SRUHPC beam specimens with rectangular section. Based on test results and theoretical derivations, a calculation method for the flexural capacity of SRUHPC beam with rectangular section was proposed. The flexural capacities of 21 SRUHPC beam specimens with rectangular section and 111 finite element calculation models were calculated, and the calculation results were compared with the test and finite element calculation values. Analysis results indicate that the failure modes of SRUHPC beam specimens with rectangular section are all reinforced failures due to bending. The steels and longitudinal tensile reinforcements yield successively, followed by the crushing of the UHPC in the compression zone. The steels and UHPC work well together until the specimens failure. The specimens with embedded inverted T-shaped and H-shaped steels exhibit higher capacities and stiffnesses compared to those with embedded I-shaped steel, and they demonstrate better crack resistances. Compared with other specimens, under the same load, the strains and strain development rates of longitudinal reinforcements, UHPC, and steels in specimens with embedded H-shaped steels are relatively smaller. Therefore, setting upper and lower flanges in the steel within SRUHPC beam with rectangular section contributes to enhancing the flexural performance of the composite beam. The calculated results obtained by the proposed method show mean ratios of 0.972 and 1.035 compared with the test and finite element calculation values, with variances of 0.009 and 0.002, respectively. The research results can provide theoretical supports for the promotion and application of SRUHPC beams with rectangular section in practical engineering and the formulations of codes and regulations.
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图 2 计算弯矩与试验弯矩的比值
Figure 2. Ratios of calculated bending moments to test bending moments
图 9 跨中截面沿竖向的型钢应变分布
Figure 9. Strain distributions of steels along vertical direction at mid-span section
图 10 跨中截面沿竖向的UHPC应变分布
Figure 10. Strain distributions of UHPC along vertical direction at mid-span section
图 18 抗弯承载力计算值与试验值的比值
Figure 18. Ratios of calculated flexural capacities to test values
图 20 有限元与实测荷载-挠度曲线对比
Figure 20. Comparison of load-deflection curves between finite element and test
图 21 抗弯承载力公式计算值与有限元结果对比
Figure 21. Comparison between calculated flexural capacities by formula and finite element results
表 1 试件详细参数
Table 1. Detailed parameters of specimens
数据来源 试件编号 截面尺寸/mm 计算跨径/mm 型钢型号及布置方式 含钢率/% 受拉纵筋型号 fa/MPa fy/MPa fcu/MPa 文献[18] B-1 150×250 1 600 H150×60×6×8，居中 4.7 2Φ14 260.5 435.0 109.6 B-2 150×250 1 600 H150×60×6×8，居中 4.7 2Φ16 260.5 426.0 109.6 B-3 150×250 1 600 H150×60×6×8，居中 4.7 2Φ18 260.5 447.0 109.6 B-4 150×250 1 600 H150×60×6×8，下偏20 mm 4.7 2Φ14 260.5 435.0 109.6 B-5 150×250 1 600 H150×60×6×6，居中 4.1 2Φ14 266.0 435.0 109.6 B-6 150×250 1 600 H150×75×6×8，居中 5.3 2Φ14 260.5 435.0 109.6 B-7 150×250 1 600 H150×60×6×8，下偏20 mm 4.7 2Φ14 358.0 435.0 109.6 B-8 150×250 1 600 H150×75×6×8，居中 5.3 2Φ14 358.0 435.0 109.6 文献[19] L1 200×300 3 200 I20a，居中 5.9 2Φ12 246.0 389.0 122.7 L2 200×300 3 200 I20a，居中 5.9 2Φ12 246.0 389.0 154.7 L3 200×300 3 200 I20a，居中 5.9 2Φ12 246.0 389.0 176.4 L4 200×300 3 200 I20b，居中 6.6 2Φ12 246.0 389.0 122.7 L5 200×300 3 200 I20b，居中 6.6 2Φ12 246.0 389.0 154.7 L6 200×300 3 200 I20b，居中 6.6 2Φ12 246.0 389.0 176.4 文献[20] SRC-1 150×200 1 800 I14，居中 7.2 246.0 127.3 SRC-2 150×200 1 800 I14，居中 7.2 246.0 146.2 SRC-3 150×200 1 800 I14，居中 7.2 246.0 176.4 
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表 2 试件荷载与挠度比较
Table 2. Comparison of load and deflection of specimens
荷载或挠度 SU SU-T SU-LF SU-DF 开裂荷载Pcr/kN 60.0 60.0 60.0 60.0 主裂缝宽度达到0.2 mm荷载Pcr, 0.2/kN 140.0 285.0 385.0 403.3 极限荷载Pu/kN 380.0 396.0 477.0 516.0 型钢受压部分屈服荷载Psc/kN 323.6 365.4 345.0 368.2 型钢受拉部分屈服荷载Pst/kN 235.6 264.3 278.5 271.0 受压纵筋屈服荷载Prc/kN 357.1 395.0 442.2 466.2 受拉纵筋屈服荷载Prt/kN 305.3 374.2 404.6 431.7 Pcr对应的跨中挠度Δcr/mm 0.8 0.3 0.8 0.4 Pcr, 0.2对应的跨中挠度Δcr, 0.2/mm 2.2 3.8 6.5 4.4 Pu对应的跨中挠度Δu/mm 9.6 11.6 14.0 12.6 Psc对应的跨中挠度Δsc/mm 5.2 6.0 5.6 3.7 Pst对应的跨中挠度Δst/mm 3.3 3.5 4.3 2.3 Prc对应的跨中挠度Δrc/mm 6.8 11.2 8.5 6.4 Prt对应的跨中挠度Δrt/mm 4.7 6.6 7.0 5.2
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表 3 试件计算结果
Table 3. Calculation results of specimens
试件编号 含钢率/% Me/(kN·m) Mc/(kN·m) Mc/Me B-1 4.7 97.50 95.38 0.978 B-2 4.7 105.10 101.45 0.965 B-3 4.7 118.40 110.51 0.933 B-4 4.7 106.50 88.40 0.830 B-5 4.1 89.20 91.52 1.026 B-6 5.3 104.60 99.79 0.954 B-7 4.7 119.60 100.05 0.837 B-8 5.3 115.10 91.50 0.795 L1 5.9 179.44 173.67 0.968 L2 5.9 189.12 192.60 1.018 L3 5.9 199.76 205.33 1.028 L4 6.6 203.60 175.85 0.864 L5 6.6 218.96 193.67 0.885 L6 6.6 235.52 205.54 0.873 SRC-1 7.2 38.70 44.23 1.143 SRC-2 7.2 40.40 45.66 1.130 SRC-3 7.2 42.60 46.31 1.087 SU 11.0 114.00 113.81 0.998 SU-T 8.7 118.80 118.48 0.997 SU-LF 13.1 143.10 146.28 1.022 SU-DF 15.3 154.80 166.76 1.077
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